Context: Cylinder with radius $r$ and height $h$. Second cylinder has volume $576$ times as large. Find $R$ and $H$.

Answer: C: $R = 8r$ and $H = 9h$

Why: $\pi R^2 H = 576\pi r^2 h \Rightarrow R^2 H = 576 r^2 h$. Factor $576 = 64 \times 9$. If $R = 8r$, then $R^2 = 64r^2$; if $H = 9h$, then $64r^2 \cdot 9h = 576r^2h$. ✓

Traps: A gives $9^2 \times 8 = 648 \neq 576$. B and D produce values far exceeding 576.